Broad Infinity

Paul Blain Levy p.b.levy at
Fri Jan 8 20:17:34 EST 2021

Dear all,

I've just written the following paper and posted it at

(A slightly older version is on arXiv.)

Comments are welcome.  Do you agree with me that Broad Infinity is an 
intuitive axiom scheme?



Broad Infinity and Generation Principles

This paper introduces Broad Infinity, a new and arguably intuitive axiom 
scheme.  It states that ``broad numbers'', i.e.\ three-dimensional trees 
whose growth is controlled, form a set. If the Axiom of Choice is 
assumed, Broad Infinity is equivalent to the Ord-is-Mahlo scheme: every 
closed unbounded class of ordinals contains a regular ordinal.

   Whereas the axiom of Infinity leads to generation principles for 
families, sets and ordinals, Broad Infinity leads to more advanced 
versions of these principles.  The paper relates these principles under 
various prior assumptions: the Axiom of Choice, the Law of Excluded 
Middle, and weaker assumptions.

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